Hey Heather! You should be able to do exactly that, yes. I don’t even think you’d need to copy the old PRO folder unless you want it as a backup. If you rename that to something else and then attempt to upload the 3.0.5 PRO folder it should work smoothly.
Keep in mind you’ll also need the latest core The Events Calendar, too. That’s at 3.0.3 as of today and I’d recommend upgrading that one before doing PRO.
Hope that helps. Let me know if it doesn’t, or if you have other questions here.